In this paper, we show that the $(3k+4)$-dimensional Weisfeiler--Leman algorithm can identify graphs of treewidth $k$ in $O(\log n)$ rounds. This improves the result of Grohe & Verbitsky (ICALP 2006), who previously established the analogous result for $(4k+3)$-dimensional Weisfeiler--Leman. In light of the equivalence between Weisfeiler--Leman and the logic $\textsf{FO} + \textsf{C}$ (Cai, F\"urer, & Immerman, Combinatorica 1992), we obtain an improvement in the descriptive complexity for graphs of treewidth $k$. Precisely, if $G$ is a graph of treewidth $k$, then there exists a $(3k+5)$-variable formula $\varphi$ in $\textsf{FO} + \textsf{C}$ with quantifier depth $O(\log n)$ that identifies $G$ up to isomorphism.

翻译：在本文中,我们展示了美元( 3k+4) 的维维- 利曼算法能够用美元( log n) 圆圆来识别树枝美元( 3k+4) 的图表。 这改善了Grohe & Verbitsky( ICEP 2006) 的结果, 后者先前为 $( 4k+3) 的维维- 莱曼建立了类似的结果。 根据 Weisfeiler- Leman 和逻辑 $\ textsf{ FO} +\ textsf{ C}$( Cai, F\ " urer, & Immerman, Compatratorica 1992) 之间的等值, 我们得到了树枝图描述复杂性的改进。 如果$( 4k+3k+5) 美元( 3k+5) 美元( $\ varphi) 的公式在 $\ textsf{ FO} +\ textsf{C} $( textsf} $( $) rotictertictercterclecter $ OO ( nlog) $\ gentrm.</s>